FOR MODEL-BASED CONTROL DESIGN, CLOSED-LOOP IDENTIFICATION GIVES BETTER PERFORMANCE

We compare open loop versus closed loop identification when the identi fied model is used for control design, and when the system itself belo ngs to the model class, so that only variance errors are relevant. Our measure of controller performance (which is used as our design criter ion for identification) is the variance of the error between the outpu t of the ideal closed loop system (with the ideal controller) and that of the actual closed loop system (with the controller computed from t he identified model). Under those conditions, we show that, when the c ontroller is a smooth function of the input-output dynamics and the di sturbance spectrum, the best controller performance is achieved by per forming the identification in closed loop with an operating controller that we characterize. For minimum variance and model reference contro l design cirteria, we show that this 'optimal operating controller for identification' is the ideal controller. This then leads to a subopti mal but feasible iterative scheme. Copyright (C) 1996 Elsevier Science Ltd.